Week 15 - Bonds Flashcards
What is the bond indenture?
a legal contract between a bond issuing company and bondholders
What does the bond indenture include?
- basic terms of the bonds
- total amount of bonds issued
- a description of the bond security, or whether the bond is secured or unsecured
- sinking fund provisions
- embedded options (call/ put/ convertible provisions)
- details of protective covenants (restrictions and obligations)
What are two bond classifications?
- security
- seniority
What are different types of bonds based on their security and features
collateral - secured by financial securities
mortgage - secured by real property, normally land or buildings
debentures - unsecured
notes - unsecured debt with original maturity less than 10 years
What are collateralised bonds?
These bonds are backed by specific financial assets, such as stocks, bonds, or other securities. In case the issuer defaults, the bondholders can claim the underlying collateral.
What are mortgage bonds?
These bonds are secured by real estate, such as land or buildings. If the issuer defaults, bondholders can take possession of the property or land to recover their investment.
What are debentures (unsecured)?
These bonds are not backed by any collateral or specific assets. Instead, they are backed only by the creditworthiness of the issuer. Debentures tend to be riskier for bondholders than secured bonds.
What are notes (Unsecured Debt with Maturity Under 10 Years)?
Notes are short-term debt instruments, usually with a maturity of less than 10 years. Like debentures, they are unsecured, meaning they are not backed by collateral.
What is the seniority of a bond?
refers to the order in which bondholders are paid in case of liquidation or bankruptcy of the issuer.
The seniority determines the priority of claims on the issuer’s assets and income.
What typical seniority structure are involved in bonds?
Senior bonds and subordinated (Junior) bonds
What are senior bonds?
These are the highest-ranking bonds in terms of repayment priority. Senior bondholders are paid first in the event of liquidation. These bonds are usually secured (backed by collateral), offering a lower risk to investors.
What are subordinated (junior) bonds?
These bonds are ranked lower than senior bonds and have a lower claim on the issuer’s assets in case of bankruptcy. They carry a higher risk and typically offer higher interest rates to compensate for this increased risk.
What does the required return from a bond depend on?
its risks characteristics
What do these risk characteristics include?
(chat gpt)
- Credit risk
- Interest rate risk (market risk)
- Inflation risk
- Liquidity risk
- Time to maturity
- Tax considerations
- Issuers financial strength and stability
- Economic and market conditions
How is coupon rate linked to risk characteristics?
coupon rate is also a function of risk characteristics of a bond, but only when issued
What are zero-coupon bonds?
their coupon rate is 0%, make no periodic interest (coupon) payments
What are zero-coupon bonds also called?
zeroes, or deep discount bonds
What does zero-coupon bonds entire yield to maturity come from?
the difference between the bonds purchase price (the price at which it is bought) and the par value (the amount paid at maturity)
since zero-coupon bonds do not make periodic interest payments, all the return to the investor is earned through this price appreciation over time
cannot sell for more than par value
Zero coupon bond example: What is the present value of a 10 year pure discount bond paying £1,000 at maturity if the appropriate interest rate is currently 5%, 10% or 15%
using the formula PV = F/(1+r)^t
if interest rates are 5%, PV = £613.91
if interest rates are 10%, PV = £385.54
if interest rates are 15%, PV = £247.18
What are floating rate bonds?
adjust their interest payments (coupons) at regular intervals, typically every 3 to 6 months, aligning with current market rates
When do coupon rates float?
coupon rate floats depending on some index value, there is less price risk with floating rate bonds
the coupon floats, so is less likely to differ substantially from the yield-to-maturity
coupons may have a ‘collar’ - the rate cannot go above a specified ‘ceiling’ or below a specified ‘floor’
What are semi-annual coupons?
a bond pays interest twice a year instead of once annually, bonds issued in the US/ UK usually do this
What is an effective annual yield?
EAY, used for bonds, investments and securities with compounding returns
Represents the true annual return on an investment, considering compounding
What is effective annual rate (EAR)?
used for loans, saving accounts, credit cards and mortgages
Represents the true interest rate a borrower pays or an investor earns after compounding
Semi annual coupons, find the bond price and EAY (effective annual yield):
Suppose time to maturity = 7 years
Coupon rate = 14%
Face Value = £1000
Yield to maturity quoted at 16% (APR)
Coupon payment = 0.14 x 1000 = 140 (per annum)
1st coupon 70
2nd coupon = 70
T= 7 years -> t=14 (14 coupons in 7 years)
YTM = 16% -> semi annual rate = 8%
Bond Price = 70/0.08 (1- 1/(1+0.08)^14) + 1000/(1+0.08)^14
= 918.56
EAY = (1+ 0.16/2)^2 -1 =0.1664 = 16.64%
What are embedded options?
special features built into bonds or other financial instruments that give either the issuer or investor certain rights
these options affect the bond’s price, yield and risk profile
What are the 3 types of embedded options?
- Callable
- Putable
- Convertible
What are callable bonds?
grants the issuers the right to retire (redeem/repay) the bond before scheduled maturity date
allows the investors to change the maturity of a bond
Eg: A company issues a 10-year bond but reserves the right to call (redeem) it after 5 years if interest rates decline.
What are putable bonds?
it grants the bondholders the right to sell the bond back to the issuers at par value on designated date
allows the investors to change the maturity of a bond
Eg: An investor buys a 20-year bond but can put (sell) it back to the issuer after 10 years.
What are convertible bonds?
gives the bondholders right to exchange the bond for common stock at a pre-specified price
allows the investors to take advantage of favourable movements in the stock price
Eg: A bondholder holding a $1,000 convertible bond can exchange it for 50 company shares if the stock price rises above a certain level.
Between secured debt and debenture which would have a higher coupon rate?
debenture since there is no collateral there and is riskier
Between subordinated debenture and senior debt which would have a higher coupon rate?
Subordinated debt implies we are junior creditors to someone else, therefore being junior we want to demand higher coupons
Since subordinated debentures are riskier due to their lower ranking in the capital structure, investors demand a higher return (coupon rate) as compensation for taking on the additional risk.
Between a bond with a sinking fund and bond without a sinking fund which would have a higher coupon rate?
A bond without a sinking fund would typically have a higher coupon rate compared to a bond with a sinking fund.
Investors perceive bonds with a sinking fund as less risky since there is a structured plan for repayment, making it more likely that they will receive their principal back.
Between a callable and non- callable bond which would have a higher coupon rate?
A callable bond would typically have a higher coupon rate compared to a non-callable bond.
Non-callable bonds, which do not have early redemption risk, typically have lower coupon rates because investors are assured of receiving interest payments for the full term.
Do bonds vary in taxation?
some bonds incur lower or no taxes than others
for example, in the US municipal bonds are exempt from most taxes
where lower tax rates apply, yields are lower as investors dont demand additional yield to be compensated for tax
comparisons of bonds must use after-tax yields
What are the 5 key characteristics of the bond market, specifically the secondary market for bonds
- Primarily Over-the-Counter (OTC) transactions
- Large number of bond issues, but low trading volume per issue
- Difficult to get up-to-date prices
- Government Bonds are an exception
- U.S. Treasury bond market is the largest by trading volume
What are bonds mostly traded through?
Unlike stocks, which are often traded on exchanges, bonds are mostly traded OTC through dealers and brokers who are connected electronically
Why are there large number of bond issues, but low trading volume per issue?
There are thousands of different bonds issued by governments, municipalities, and corporations, but each bond may not trade frequently.
Why is it difficult to get up-to-date prices?
Since most bonds trade OTC and not on centralised exchanges, pricing transparency is limited, especially for smaller company bonds or municipal bonds
Why are government bonds an exception?
Government bonds (like U.S. Treasuries) are more actively traded, and their prices are easier to obtain
Why is the US treasury bond market the largest by trading volume?
The U.S. Treasury market is the most liquid and largest securities market globally, with trillions of dollars in daily trading volume
What is the clean price of a bond?
The quoted price of a bond, excluding accrued interest
What is the dirty price of a bond?
The total amount the buyer actually pays, which includes accrued interest
Example bond quotations and prices
You buy a bond with a 12% coupon paid semi-annually and you pay £1,080 (purchase price, dirty price). The next coupon is due in 4 months and will be £60 (semi-annual coupon payment)
The accrued interest paid is the fraction of time since the last coupon payment (2 months) × the next coupon (£60)
Accrued interest is therefore 2/6 × £60 = £20.
Dirty price = Clean price + Accrued interest
The clean price would be £1,060
So, the quoted price is £1,060 (clean price), but the amount paid is £1,080 (dirty price), because the buyer compensates the seller for the interest that has accrued since the last coupon payment
Example of accrued interest: A bond has a coupon rate of 7.5%, semi-annual coupons and a clean price of £915. If the next coupon payment is due in 3 months, what is the invoice (dirty) price?
Coupon payments are £75 a year, so £37.50 twice a year.
Next payment is in 3 months, so accrued interest is 37.50/2 = 18.75
Invoice price is £915 + £18.75 = £933.75
What is the bid price?
The price a dealer is willing to pay to buy the bond from an investor
What is the ask price (offer price)?
The price at which the dealer is willing to sell the bond (this is higher than the bid price)
What is the bid-ask spread?
The difference between the ask price and the bid price—this represents the dealer’s profit margin
What is the ask yield?
The yield to maturity (YTM) based on the higher ask price (since you’re paying more for the bond, yield is lower)
What is the bid yield?
The YTM based on the lower bid price (since you’re buying at a lower price, yield is higher)
What are 8 major risks associated with bond investments?
- interest rate risk (this risk is by far the major risk faced by investors in the bond market)
- reinvestment risk
- default risk
- call risk
- inflation risk
- exchange rate risk
- liquidity risk
- volatility risk
What is interest rate risk also known as?
price risk
Why is there an inverse relationship between bond prices and interest rates?
When interest rates rise, the price of existing bonds tends to fall. Conversely, when interest rates fall, the price of existing bonds tends to rise
If interest rates increase, newer bonds are issued with higher coupon rates, making the existing bonds with lower rates less attractive. To compensate, the price of the older bonds must decrease to offer a competitive yield
What is interest rate risk?
the risk that changes in interest rates will affect the market price of a bond.
It is especially relevant when holding bonds until they are sold before maturity
What is the impact of interest rate risk?
If interest rates rise after you purchase a bond, you may be forced to sell the bond at a lower price, resulting in a capital loss
What are 2 factors that influence interest rate risk?
- time to maturity
- coupon rate
How does time to maturity influence interest rate risk?
The longer the time to maturity, the greater the interest rate risk
Bonds with longer maturities are more sensitive to interest rate changes because they lock in the coupon rate for a longer period
Example of time to maturity influencing interest rate risk
A bond with 10 years to maturity is much more affected by a 1% change in interest rates than a bond with just 2 years to maturity. This is because there are more years of fixed payments that could become less valuable if interest rates rise
How does coupon rate influence interest rate risk?
The lower the coupon rate, the greater the interest rate risk
A bond with a low coupon rate is more sensitive to interest rate changes because its payments are smaller. Most of the bond’s value is derived from its face value (principal) that is repaid at maturity. If interest rates rise, the smaller coupon payments mean the bond will lose value more rapidly compared to a high-coupon bond, where the majority of the value is in the periodic coupon payments
Example of coupon rate influencing interest rate risk
A bond with a 4% coupon rate will be more affected by a rise in interest rates than a bond with a 6% coupon rate, as the higher coupon bond’s payments provide more value in the short term
How sensitive is the bond the longer the maturity of the bond?
more price sensitive the bond is to
interest rate changes
What is the intuition behind interest rate risk and coupon rates?
a bond with a higher coupon has a larger cash flow earlier in its life, so its value is less
sensitive to changes in discount rates
Why do lower coupon bonds have higher interest rate risk?
A bond with a lower coupon has more of its value tied to the final principal payment, making its price more affected by changes in the discount rate (interest rate)
What is credit risk?
he risk that the bond issuer fails to make interest or principal payments on time
What is credit risk also known as?
default risk
What is the calculation of the value of the bond using YTM based on?
the assumption that there is no possibility of default
assumes that all coupon payments and the principal will be paid in full
What does higher credit mean for required return?
if there is any credit risk, investors will require a higher return
Investors demand a higher yield (risk premium) to compensate for the risk of potential default.
What is the credit spread?
This extra yield over a “risk-free” bond (such as U.S. Treasuries)
Example of credit risk
A U.S. Treasury bond might yield 4% (virtually no credit risk).
A corporate bond from a lower-rated company might yield 8% because investors require extra compensation for the risk of default
What are bond ratings?
Bond ratings measure default risk—the likelihood that an issuer will fail to make interest or principal payments on time.
These ratings are provided by:
Moody’s Investor Service
Standard & Poor’s (S&P)
Fitch Ratings
What are the bond rating categories?
Investment-grade bonds (BBB-/Baa3 and above) are considered low risk.
Junk bonds (high-yield bonds) (BB+/Ba1 and below) have higher risk but offer higher returns.
A “D” rating means the issuer has defaulted.
What are 4 reasons why financial managers care about their firm’s bond ratings?
- lower borrowing costs
- access to capital
- market perception
- convenant compliance
How do bond ratings affect borrowing costs?
Higher bond ratings mean lower interest rates when issuing debt, reducing financing costs
How do bond ratings affect access to capital?
Investment-grade ratings allow firms to attract institutional investors (e.g., pension funds, mutual funds), which often cannot buy junk bonds
How do bond ratings affect market perception?
A downgrade in credit rating can cause stock and bond prices to fall, affecting investor confidence
How do bond ratings affect covenant compliance?
Some loan agreements require firms to maintain a certain credit rating
What are nominal interest rates?
The stated interest rate without adjusting for inflation
What financial rates are almost always quoted in nominal terms?
interest rates, discount rates and rates of
return
What does the nominal rate represent?
The raw return in currency terms (£, $, €)
What are real interest rates?
The inflation-adjusted interest rate, showing the true change in purchasing power
What do real interest rates represent?
The actual gain in terms of what you can buy with the money
What is the fisher effect?
1 + R = (1 + r) x (1 + h)
R = r + h + r x h, where r x h is small
R ≈ r + h
R is the nominal rate on investment
r is the real rate on investment
(1+h) is the percentage change in the price level of goods - inflation rate
Example of the fisher effect: if we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?
R = (1 + r) × (1 + h) − 1
R = (1 + 0.1) × (1 + 0.08) − 1 = 0.188, or 18.8%
approximation: R = 10% + 8% = 18%
because the real return and expected inflation are relatively high, there is a significant difference between the actual Fisher Effect and the approximation
What is the term structure of interest rates?
It shows the relationship between bond yields (interest rates) and their time to maturity, assuming all other factors (credit risk, coupon size, etc.) are constant
It helps investors understand how interest rates are expected to change over time
What is the yield curve?
a graph that plots time to maturity (on the x-axis), bond yields (on the y-axis)
a graphical representation of the term structure
It reflects investor expectations about future interest rates and economic conditions.
What does an upward-sloping (normal) yield curve mean?
Long-term rates > Short-term rates
Economy is expected to grow, inflation may rise
What does a downward sloping (inverted) yield curve mean?
Long-term rates < Short-term rates
Possible recession, as investors expect lower future rates
What does a flat yield curve mean?
Long-term rates ≈ Short-term rates
Economic uncertainty; interest rates are expected to stay stable
Why does the yield curve matter?
- Predicts Economic Trends:
Normal Curve → Growth, higher inflation expected
Inverted Curve → Possible recession, as investors seek safety in long-term bonds - Affects Borrowing & Lending:
Banks lend at long-term rates and borrow at short-term rates. If the curve inverts, lending profits shrink. - Guides Investment Decisions:
Investors adjust portfolios based on expected rate changes.
What 3 factors determines the shape of the term structure?
The term structure of interest rates (and the shape of the yield curve) is influenced by three key factors:
1. real rate of interest (r)
2. inflation premium (π)
3. interest rate risk premium
What is the real rate of interest?
This is the pure time value of money after adjusting for inflation.
It represents the compensation investors require for deferring consumption.
Since the real rate does not change much in the short term, its effect on the yield curve is relatively stable
What is an example of the real rate of interest?
If the real interest rate is 2%, and there’s no inflation or risk premium, all bond yields would be around 2%, creating a flat yield curve
What is inflation premium?
Investors demand compensation for expected inflation risk over time.
If future inflation is expected to rise, long-term bond yields will be higher than short-term yields → Upward-sloping curve.
If inflation is expected to decline, long-term yields fall below short-term yields → Inverted curve
An example of inflation premium
Current inflation is 2%, but expected inflation in 10 years is 4% → Investors demand higher long-term yields.
This is why inflation expectations have a strong influence on the shape of the yield curve
What is interest rate risk premium?
Long-term bonds carry higher risk because their prices are more sensitive to interest rate changes.
Investors demand a higher yield for holding long-term bonds to compensate for this interest rate risk.
The longer the bond’s maturity, the greater the risk premium, but at a decreasing rate
Example of interest rate premium
A 1-year bond may yield 3%, while a 10-year bond yields 5% due to the additional risk premium.
However, a 30-year bond may only yield 5.5%, as the added risk premium diminishes at longer maturities
